If you intend to build the entire menu in AE, you’ll need to export a Photoshop file for use in Encore – all Encore menus are PSD files.
As for your second question, extend the duration of your comp in AE so there’s at least 10 to 15 sec (or more) of footage after your buttons appear. The looping is done in Encore, using the Loop and Loop Point properties of the menu.